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Probability that the commutator of two group elements is equal to a given element

Pournaki, M. R ; Sharif University of Technology | 2008

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  1. Type of Document: Article
  2. DOI: 10.1016/j.jpaa.2007.06.013
  3. Publisher: 2008
  4. Abstract:
  5. In this paper we study the probability that the commutator of two randomly chosen elements in a finite group is equal to a given element of that group. Explicit computations are obtained for groups G which | G′ | is prime and G′ ≤ Z (G) as well as for groups G which | G′ | is prime and G′ ∩ Z (G) = 1. This paper extends results of Rusin [see D.J. Rusin, What is the probability that two elements of a finite group commute? Pacific J. Math. 82 (1) (1979) 237-247]. © 2007 Elsevier Ltd. All rights reserved
  6. Keywords:
  7. Schur multiplier ; Finite group ; Commutativity
  8. Source: Journal of Pure and Applied Algebra ; Volume 212, Issue 4 , 2008 , Pages 727-734 ; 00224049 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S0022404907001685